Things that cauliflower people say.

No. Health obsessed people are mostly obsessed with feeling superior to others based on diet, so they won't ever stop shaming anyone who eats differently than they do. They are projecting their insecurity with themselves, and they are so insecure eating some peas might as well by drinking 2L of soda per day, because they are unable to contextualize anything appropriately, and just panic over every slightly 'wrong' thing someone else does.

Same with politics or a hobby, or anything else people seek personal validation in. Anyone who doesn't do it exactly the way they do it is invalidating them and it hurts them and they lash out.

No, they are actually correct about the effects of starchy vegetables. They have some benefits - like carrots having beta-carotene, but they are about as unhealthy as refined grains are. Maybe slightly worse. Their consumption should be kept on the lower side, and their detriments can be mitigated or even canceled out by being eaten in the same meal as other high fiber whole foods and sources of unsaturated fats.

The kneejerk reactions are justified IMO. You don't need to "minimize" peas and carrots to have a healthy diet. Obviously they shouldn't be all you eat, but that holds for pretty much all foods - balance is key.

There's several issues with your source.

First, it would have been nice of you to link to the relevant figure so others aren't forced to comb through the whole thing.

Second, it's important to point out that this data only shows correlation. The data is interesting for sure, but one should be cautious about demonizing a particular food group based on this alone, considering that the main point of the study was to analyze the health benefits of particular diets rather than food groups.
(note also that fast/fried foods got a positive score, which makes me further apprehensive about drawing quick conclusions from this data)

Third, this study focused on health professionals only. I don't know why it shouldn't generalize to the general population but it is not a given that it does.

Most importantly, it is not clear (to me at least) that peas and carrots are part of the category "starchy vegetables" according to this study. I couldn't find any explicit description of the categories, please let me know if there is one in the study or one of its sources.
From what I could find online, peas can be considered starchy vegetables, but carrots usually aren't. For instance, this site classifies both carrots and some types of peas as non-starchy.